Overview
- Provides rigorous numerical analyses for the treatment of modern applications with state-of-the-art approximation schemes
- Includes explanations of the mathematical modeling and analytical properties for the problems considered
- Simple Matlab codes allow the reader to test the numerical methods in two- and three-dimensional situations
- First book on the numerical analysis of nonlinear partial differential equations
- Includes supplementary material: sn.pub/extras
Part of the book series: Springer Series in Computational Mathematics (SSCM, volume 47)
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About this book
The description of many interesting phenomena in science and engineering leads to infinite-dimensional minimization or evolution problems that define nonlinear partial differential equations. While the development and analysis of numerical methods for linear partial differential equations is nearly complete, only few results are available in the case of nonlinear equations. This monograph devises numerical methods for nonlinear model problems arising in the mathematical description of phase transitions, large bending problems, image processing, and inelastic material behavior. For each of these problems the underlying mathematical model is discussed, the essential analytical properties are explained, and the proposed numerical method is rigorously analyzed. The practicality of the algorithms is illustrated by means of short implementations.
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Table of contents (11 chapters)
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Front Matter
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Analytical and Numerical Foundations
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Front Matter
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Approximation of Classical Formulations
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Front Matter
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Methods for Extended Formulations
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Front Matter
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Back Matter
Reviews
“This book presents an ambitious overview of modern results and trends in the field of numerical methods for nonlinear PDEs, with an emphasis on the finite element method. … The target audience of the book is postgraduates and experienced researchers. … this is an excellent monograph describing methods found at the intersection of numerical PDEs and the calculus of variations.” (Michael Neilan, SIAM Review, Vol. 58 (3), September, 2016)
“This book provides advanced students and experimental researchers with an introduction to numerical methods for nonlinear partial differential equations, in particular those originating from continuum mechanics. … This book presents a very nice transition from graduate-level material to state-of-the-art research topics. … This is a nice and well-written advanced textbook.” (Karsten Urban, Mathematical Reviews, October, 2015)
Authors and Affiliations
Bibliographic Information
Book Title: Numerical Methods for Nonlinear Partial Differential Equations
Authors: Sören Bartels
Series Title: Springer Series in Computational Mathematics
DOI: https://doi.org/10.1007/978-3-319-13797-1
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2015
Hardcover ISBN: 978-3-319-13796-4Published: 03 February 2015
Softcover ISBN: 978-3-319-35680-8Published: 22 October 2016
eBook ISBN: 978-3-319-13797-1Published: 19 January 2015
Series ISSN: 0179-3632
Series E-ISSN: 2198-3712
Edition Number: 1
Number of Pages: X, 393
Number of Illustrations: 122 b/w illustrations
Topics: Numerical Analysis, Partial Differential Equations, Algorithms, Calculus of Variations and Optimal Control; Optimization